Lock-down dispensing pumps typically rely upon the ability of the plunger to be rotated to a certain degree relative to locking structure on the pump body in order to engage and disengage the lock. In certain situations, however, it may not be possible to hold the pump body immobile using the common technique of clamping a rigid flange of the body between the closure and the upper edge of a neck on the container. Consequently, an important object of the present invention is to provide a way of rendering the pump body, and thus its associated lock structure, immobile relative to the plunger which does not rely upon that type of clamping action, inasmuch as it may or may not be available in any given situation.